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arXiv · 1809.08975

Axiomatic construction of quantum Langevin equations

Rúbia Araújo·Sascha Wald·Malte Henkel
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Abstract

A phenomenological construction of quantum Langevin equations, based on the physical criteria of (i) the canonical equal-time commutators, (ii) the Kubo formula, (iii) the virial theorem and (iv) the quantum fluctuation-dissipation theorem is presented. The case of a single harmonic oscillator coupled to a large external bath is analysed in detail. This allows to distinguish a markovian semi-classical approach, due to Bedeaux and Mazur, from a non-markovian full quantum approach, due to to Ford, Kac and Mazur. The quantum-fluctuation-dissipation theorem is seen to be incompatible with a markovian dynamics. Possible applications to the quantum spherical model are discussed.

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Rúbia Araújo, Sascha Wald, Malte Henkel. 2019-03-14. Axiomatic construction of quantum Langevin equations. https://doi.org/10.1088/1742-5468%2Fab11dc

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